When did you first encounter proof based mathematics?

In summary, when did you first encounter "proof based" mathematics in a classroom setting? Was it in high school or university/college? What year in high school or university did you encounter it? My first encounter with proofs was probably in high school (freshman-sophomore year). The proofs were very easy though, but I didn't quite grasp them. Throughout high school, the teachers kept emphasizing proofs and I got better at them. But I wouldn't say that the classes in high school were proof-based: the proofs were usually very easy and there weren't a lot). My first real proof based course was an analysis course in freshman year. The course was literally filled with proofs.
  • #36


I first encountered "proof-based mathematics" in high school in a Geometry class. The work could have been more engaging, although, and I think this would have been good for me and the other students too. I plan on learning more math with you all and on this forum. Best Pokemon, your second to last post doesn't seem appropriate but perhaps I have misunderstood your writing.
 
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  • #37


alissca123 said:
I took my first proof based course as a freshman. At my university, if you study math, physics, computer science or actuarial science, with very few exceptions, all the math courses you'll take are going to be proof based.
Which uni do you attend?
 
  • #38


Patrick Kale said:
I first encountered "proof-based mathematics" in high school in a Geometry class. The work could have been more engaging, although, and I think this would have been good for me and the other students too. I plan on learning more math with you all and on this forum. Best Pokemon, your second to last post doesn't seem appropriate but perhaps I have misunderstood your writing.

I'm sorry if I sounded that way. I was just saying that adding physics wouldn't make it more interesting.
 
  • #39


Best Pokemon said:
I've been reading a few forums and have seen many posters say "methods based" mathematics like calculus is easy. The posters would then state that "proof based" mathematics is so hard and calculus isn't high level.

So when did you first encounter "proof based" mathematics in a classroom setting? Was it in high school or university/college? What year in high school or university did you encounter it?

Edit: What grade did first encounter it (if it was in high school)?

What college/major was this person? This is an outright lie. I did many proofs in calculus.
 
  • #40


MathINTJ said:
What college/major was this person? This is an outright lie. I did many proofs in calculus.

Experiences vary, depending on district, depending on era, depending on the educational fashion of the time and place. Schools (secondary level, or college level) may have courses designed for different student levels and for different major field emphases.
 
  • #41


Best Pokemon said:
Physics schmysics! That would only make it worse, especially for girls.
For girls?
 
  • #42


Devils said:
I've read that there is a way of doing the standard school geometry problems WITHOUT the standard proof method. To make it more intuitive for kids and stop them hating maths.

Anybody know anything about this?

micromass said:
So, what do you propose? Just giving out the statements and let the kids memorize that? Yeah, that way they're going to stop hating math.

I somehow never learned proofs in school in Sinagpore. We learned a bunch of silly rules which worked, like "opposite angles are equal". So I am completely unable to do rigourous American high school geometry, although I can do the physics just fine.

I have no real idea what a proof is. There are only two proofs I have studied. One was Shannon's noisy channel theorem, and the other was Goedel's incompleteness theorem in Hofstadter's book. I read them because they didn't seem intuitive to me, whereas I was able to naively "buy" all the other "maths" I've needed.
 
  • #43


For me, first exposure was high school geometry, as for others in US. They were actually experimenting with new curriculum, so the course was probably 90% proofs.

Then, in college, it was linear algebra, then Real Analysis using Dieudonne book.

Funnny, but at least at this level (rather than research math), I found proofs very easy.
 
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  • #45


phinds said:
I think in the US at least everyone's first encounter with proof-based math is high school geometry. I remember well the delight I felt at finding that math wasn't just about algebraic equations and arithmetic. I loved doing the proofs.

I'm a freshman taking a geometry class right now, and I couldn't agree with you more! I really enjoy seeing the general theory behind math rather than just crunching numbers all day. Exponents were my nemesis in Algebra I.
 
  • #46


alissca123 said:

Lol i was suspecting that.

alissca123 said:
I took my first proof based course as a freshman. At my university, if you study math, physics, computer science or actuarial science, with very few exceptions, all the math courses you'll take are going to be proof based.

This just seemed too familiar. Facultad de Ciencias FTW!
 
<H2>1. When did you first encounter proof-based mathematics?</H2><p>I first encountered proof-based mathematics in my undergraduate studies. I took a course on abstract algebra where we learned how to construct and write mathematical proofs.</p><H2>2. What is the difference between proof-based mathematics and other types of mathematics?</H2><p>Proof-based mathematics involves using logical arguments and rigorous reasoning to prove the truth of mathematical statements, whereas other types of mathematics may rely more on computation and numerical methods.</p><H2>3. Why is proof-based mathematics important in the field of science?</H2><p>Proof-based mathematics is important in science because it provides a solid foundation for understanding and verifying scientific theories and models. It also allows for the development of new mathematical concepts and techniques that can be applied to various scientific disciplines.</p><H2>4. How do you approach constructing a mathematical proof?</H2><p>When constructing a mathematical proof, I first analyze the statement or theorem that needs to be proven. Then, I break it down into smaller, more manageable parts and use logical reasoning and previously proven theorems to build a chain of arguments that lead to the desired conclusion.</p><H2>5. What advice do you have for someone new to proof-based mathematics?</H2><p>My advice would be to practice, practice, practice! Start with simpler proofs and work your way up to more complex ones. Also, make sure to thoroughly understand the definitions and theorems before attempting to prove them. And don't be afraid to ask for help or seek out additional resources if needed.</p>

1. When did you first encounter proof-based mathematics?

I first encountered proof-based mathematics in my undergraduate studies. I took a course on abstract algebra where we learned how to construct and write mathematical proofs.

2. What is the difference between proof-based mathematics and other types of mathematics?

Proof-based mathematics involves using logical arguments and rigorous reasoning to prove the truth of mathematical statements, whereas other types of mathematics may rely more on computation and numerical methods.

3. Why is proof-based mathematics important in the field of science?

Proof-based mathematics is important in science because it provides a solid foundation for understanding and verifying scientific theories and models. It also allows for the development of new mathematical concepts and techniques that can be applied to various scientific disciplines.

4. How do you approach constructing a mathematical proof?

When constructing a mathematical proof, I first analyze the statement or theorem that needs to be proven. Then, I break it down into smaller, more manageable parts and use logical reasoning and previously proven theorems to build a chain of arguments that lead to the desired conclusion.

5. What advice do you have for someone new to proof-based mathematics?

My advice would be to practice, practice, practice! Start with simpler proofs and work your way up to more complex ones. Also, make sure to thoroughly understand the definitions and theorems before attempting to prove them. And don't be afraid to ask for help or seek out additional resources if needed.

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